Face problem in cube, edit mode
Go into edit mode, and press A to select all the vertices. Press the spacebar and type in "Triangulate Faces," and that should fix the problem. 

Blender sometimes has problems calculating bent rectangles (technically known as quads), because they can be made out of two triangles bent one out of two ways. Take this plane for example: 

It can be made of either these triangles: 

Or these triangles: 



As you can see, both versions use the same exact vertex locations, but achieve completely different effects. However, Blender doesn't know which one to choose. In your case, Blender gets confused and decides to basically fold the weird looking face in half, instead of making it concave. By using "Triangulate Faces," you are basically asking Blender to turn each face into a specific set of triangles, so that way it doesn't get confused about the possibilities. In the end, your cube should look like this: 

I hope I helped you, and let me know if you have any questions.

Happy Blendering,
Graves Broderick